Data integration name of best practices to avoid corruption, caused by becoming out of sync?

I have identified an issue in the design of a system and I am trying to find the right language to describe the cause of the issue so I can report it to managers, and get the issue fixed. The problem is we have a web service syncing data by copying changes (based on a datetime of last edit column) in a student enrollments table from one system to another system. But because the sources system deletes rows when a student drops a subject, drops are not being synced. To be able to detect the drops the system needs to maintain a state of what it has copied to the second system so it can recognize when rows have been dropped or needs to validate that they tables are in sync, but I am not sure how to describe this and reference a specific best practice or methodology to backup my argument. Does anyone know the name of the best practices or data integrity rules that would prevent this type of logical error in the design?